Calculus (2nd Edition) by Gilbert Strang
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About this book :-
Calculus (2nd Edition) written by
Gilbert Strang .
This textbook is a well-organized treatise on calculus. The author intuitively provides detailed and intensive explanations fulfilling beginner’s needs. The book is both useful as a reference and a self-taught manual of calculus. Chapter 1: Introduction to Calculus; Chapter 2: Derivatives; Chapter 3: Applications of the Derivative; Chapter 4: The Chain Rule; Chapter 5: Integrals; Chapter 6: Exponentials and Logarithms; Chapter 7: Techniques of Integration; Chapter 8: Applications of the Integral; Chapter 9: Polar Coordinates and Complex Numbers; Chapter 10: Infinite Series; Chapter 11: Vectors and Matrices; Chapter 12: Motion along a Curve; Chapter 13: Partial Derivatives; Chapter 14: Multiple Integrals; Chapter 15: Vector Calculus; Chapter 16: Mathematics after Calculus.
Book Detail :-
Author(s): Gilbert Strang
Publisher: Wellesley College
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About Author :-
The author William Gilbert Strang was born in 1934, usually known as simply Gilbert Strang or Gil Strang, is an American mathematician, with contributions to finite element theory, the calculus of variations, wavelet analysis and linear algebra. He has made many contributions to mathematics education, including publishing seven mathematics textbooks and one monograph. Strang is the MathWorks Professor of Mathematics at the Massachusetts Institute of Technology. He teaches Introduction to Linear Algebra and Computational Science and Engineering and his lectures are freely available through MIT OpenCourseWare.
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Book Contents :-
Calculus (2nd Edition) written by
cover the following topics.
Introduction to Calculus
Velocity and Distance, Calculus Without Limits, The Velocity at an Instant, Circular Motion, A Review of Trigonometry, A Thousand Points of Light, Computing in Calculus
The Derivative of a Function, Powers and Polynomials, The Slope and the Tangent Line, Derivative of the Sine and Cosine, The Product and Quotient and Power Rules, Limits, Continuous Functions
Applications of the Derivative
Linear Approximation, Maximum and Minimum Problems, Second Derivatives: Minimum vs. Maximum, Graphs, Ellipses, Parabolas, and Hyperbolas, Iterations x,+ ,= F(x,), Newton's Method and Chaos, The Mean Value Theorem and l'H8pital's Rule
The Chain Rule
Derivatives by the Chain Rule, Implicit Differentiation and Related Rates, Inverse Functions and Their Derivatives, Inverses of Trigonometric Functions,
The Idea of the Integral, Antiderivatives, Summation vs. Integration, Indefinite Integrals and Substitutions, The Definite Integral, Properties of the Integral and the Average Value, The Fundamental Theorem and Its Consequences, Numerical Integration
Exponentials and Logarithms
An Overview, The Exponential ex, Growth and Decay in Science and Economics, Logarithms, Separable Equations Including the Logistic Equation, Powers Instead of Exponentials, Hyperbolic Functions
Techniques of Integration
Integration by Parts, Trigonometric Integrals, Trigonometric Substitutions, Partial Fractions, Improper Integrals
Applications of the Integral
Areas and Volumes by Slices, Length of a Plane Curve, Area of a Surface of Revolution, Probability and Calculus, Masses and Moments, Force, Work, and Energy
Polar Coordinates and Complex Numbers
Polar Coordinates, Polar Equations and Graphs, Slope, Length, and Area for Polar Curves, Complex Numbers
The Geometric Series, Convergence Tests: Positive Series, Convergence Tests: All Series, The Taylor Series for ex, sin x, and cos x, Power Series
Vectors and Matrices
Vectors and Dot Products, Planes and Projections, Cross Products and Determinants, Matrices and Linear Equations, Linear Algebra in Three Dimensions
Motion along a Curve
The Position Vector, Plane Motion: Projectiles and Cycloids, Tangent Vector and Normal Vector, Polar Coordinates and Planetary Motion
Surfaces and Level Curves, Partial Derivatives, Tangent Planes and Linear Approximations, Directional Derivatives and Gradients, The Chain Rule, Maxima, Minima, and Saddle Points
Constraints and Lagrange Multipliers
Multiple Integrals, Double Integrals, Changing to Better Coordinates, Triple Integrals, Cylindrical and Spherical Coordinates
Vector Fields, Line Integrals, Green's Theorem, Surface Integrals, The Divergence Theorem, Stokes' Theorem and the Curl of F
Mathematics after Calculus
Linear Algebra, Differential Equations, Discrete Mathematics, Study Guide For Chapter 1, Answers to Odd-Numbered Problems
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